Poincaré's equations for Cosserat shells  application to locomotion of cephalopods  Federico Renda, Frederic Boyer

Author: Federico Renda, Frederic Boyer
DIO URL: http://dx.doi.org/10.1007/9783319250403_55
Video: http://www.youtube.com/watch?v=RXF12CcGOwU
Slides: Boyer_ Poincaré equations Cosserat shells.pdf
Presentation: https://www.see.asso.fr/node/14356
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In 1901 Henri Poincaré proposed a new set of equations for mechanics. These equations are a generalization of Lagrange equations to a system whose configuration space is a Lie group, which is not necessarily commutative. Since then, this result has been extensively refined by the Lagrangian reduction theory. In this article, we show the relations between these equations and continuous Cosserat media, i.e. media for which the conventional model of point particle is replaced by a rigid body of small volume named microstructure. In particular, we will see that the usual shell balance equations of nonlinear structural dynamics can be easily derived from the Poincaré’s result. This framework is illustrated through the simulation of a simplified model of cephalopod swimming.